Hexagon cut pyramid

Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge is 12 cm, and the side edge length is 41 cm.

Correct answer:

V = 44790.6808 cm³

a_{1} = 30 cm a_{2} = 12 cm s = 41 cm n = 6 S_{1} = n \cdot 3 / 4 \cdot a_{1}^{2} = 6 \cdot 3 / 4 \cdot 3 0^{2} = 13503 cm^{2} ≐ 2338.2686 cm^{2} S_{2} = n \cdot 3 / 4 \cdot a_{2}^{2} = 6 \cdot 3 / 4 \cdot 1 2^{2} = 2163 cm^{2} ≐ 374.123 cm^{2} h = s^{2} - (a_{1} - a_{2})^{2} = 4 1^{2} - (30 - 12)^{2} = 1357 cm ≐ 36.8375 cm h_{2} = h \cdot a_{2} / (a_{1} - a_{2}) = 36.8375 \cdot 12 / (30 - 12) ≐ 24.5583 cm h_{1} = h + h_{2} = 36.8375 + 24.5583 ≐ 61.3958 cm V_{1} = \frac{1}{3} \cdot S_{1} \cdot h_{1} = \frac{1}{3} \cdot 2338.2686 \cdot 61.3958 ≐ 47853.2914 cm^{3} V_{2} = \frac{1}{3} \cdot S_{2} \cdot h_{2} = \frac{1}{3} \cdot 374.123 \cdot 24.5583 = 484071 cm^{3} ≐ 3062.6107 cm^{3} V = V_{1} - V_{2} = 47853.2914 - 3062.6107 ≐ 44790.6808 cm^{3} Verifying Solution: V_{3} = \frac{h}{3} \cdot (S_{1} + S_{1} \cdot S_{2} + S_{2}) = \frac{3 6 . 8 3 7 5}{3} \cdot (2338.2686 + 2338.2686 \cdot 374.123 + 374.123) ≐ 44790.6808 cm^{3} V_{3} = V

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